solve: 4y/y-3 - 3/1 = 3y-1/y+3?

Question

and/or solve: 3/x+3 =12x+19/x^2+7x+12 - 5/x+4

Answer 1

4y/(y-3) - (3/1) = (3y-1)/(y+3)

multiply both sides by (y+3)(y-3) to get rid of the fractions:
4y(y+3) -3(y+3)(y-3) = (3y-1)(y-3)

now start by multiplying everything out (be careful to watch the signs)
4y^2 + 12y -3(y^2 -9) = 3y^2 - 4y +3
4y^2 + 12y -3y^2 +9 = 3y^2 - 4y +3

now combine like terms:
y^2 + 12y +9 = 3y^2 - 4y +3

now set the equation equal to zero by moving everything over to the left side
y^2 + 12y +9 -3y^2 +4y -3 = 0

combine like terms again:
-2y^2 +16y +6 = 0

now factor:
-2(y^2 + 8y + 3) = 0

finish factoring by completing the square or use the quadradic formula:
x= (-b + or - squareroot(b^2 - 4ac))/2a

Answer 2

ok, so the 1st element you p.c. to attempt to do is get all of those y's out of the denominators so as that they are much less annoying to handle. because of the fact the main y's are in the denominator on the desirable hand area (a million/y^2), it may well be superb to do away with the y^2 in the denominator. to try this, in basic terms multiply the two area of the equation by y^2 so the desirable hand area would be y^2/y^2 = a million. once you multiply the left hand area by y^2, you get y^2/(3y) - y^2/(4y). on the grounds that there are y's in the numerators and denominators of the two a sort of words, you could cancel a number of them. This leaves you with y/3 - y/4 = a million for the equation, putting the left and ideal factors jointly. Now, to combine the y words on the left area, you could detect a easy denominator. the finest is in basic terms 3 * 4 = 12. To make y/3 = something over 12, you could multiply it by 4/4 to make the denominator 12 (on the grounds that 3 * 4 = 12). This leaves you with 4y/12. in addition, the different term will become -3y/12. So the equation is now 4y/12 - 3y/12 = a million. you could now upload the climate on the left jointly on the grounds that they have a easy denominator, so which you get (4y - 3y)/12 = a million. properly 4y - 3y is in basic terms y, so this simplifies to y/12 = a million. Now in basic terms multiply the two area by 12 to do away with the 12 in the denominator on the left, and you have y = 12!

Answer 3

Taking the top equation:
4y/y is 4
4-3-3/1= -2 (no brackets so multiply and divide before adding and substracting)
So -2 = 3y-1/y+3
take 3 from both sides
-5 = 3y -1/y
Multiple both sides by y
-5y= 3y² -y/y
Rearranging
3y²+5y-1 =0
Using the formula that y= (-b+/-sqrt(b²-4ac))/2a where a=3,b=5 and c=-1 we have y = 0.1805 or -1.847
Both of these answers inserted into the original formula give the correct result.

Answer 4

Hun ... for the first part is the answer 2/3. This is a wild try. I hope I solved it correctly.

Answer 5

Please use parentheses so we can tell what belongs in the numerator and what is in the denominator.